솔루션피아

$$\begin{cases} \vec v_0 &= (18.0\ut{m/s},40.0\degree)\\ \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{aligned} \vec v_0 &= (18.0\ut{m/s},40.0\degree)\\ &=18\cos40\degree\i+ 18\sin40\degree\j\\ \end{aligned}$$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ &= 18\sin40\degree t+\frac{1}{2}(-g)t^2\\ &= 18\sin40\degree t-\frac{1}{2}gt^2\\ \end{aligned}$$ $$ \vec..

$$\begin{cases} \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} \Delta x &= 77.0\ut{m}\\ \Delta y &= 0\\ \theta &= 12.0\degree\\ \end{cases}$$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ 0 &= (v_0\sin\theta) t+\frac{1}{2}(-g)t^2\\ 0 &= v_0\sin\theta -\frac{1}{2}gt\\ t &= \frac{2v_0}{g}\sin\theta\\ \end{aligned}$$ $$\begin{aligned} \Delta x &= v_xt,\\ ..

$$\begin{cases} \vec a &= -g\j\\ g &= 9.8\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} \Delta x &= 8.95\ut{m}\\ v_0 &= 9.5\ut{m/s}\\ \end{cases}$$ $$\begin{cases} v_x &= v_0\cos\theta\\ v_y &= v_0\sin\theta\\ \end{cases}$$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ 0 &= (v_0\sin\theta) t+\frac{1}{2}(-g)t^2\\ 0 &= v_0\sin\theta -\frac{1}{2}gt\\ t &= \frac{2v_0}{g}\sin\theta\\ \end{al..

$$\begin{cases} \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$\begin{cases} h &= 40.4\ut{m}\\ \vec v_0 &= 285\i\ut{m/s}\\ \end{cases}$$ (a) $t=?$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ -h &= (0)t+\frac{1}{2}(-g)t^2\\ h &= \frac{1}{2}gt^2\\ t &=\sqrt{\frac{2h}{g}}\\ &\approx2.8704193075\ut{s}\\ &\approx2.87\ut{s} \end{aligned}$$ (b) $\Delta x=?$ $$\begin{alig..

$$\begin{cases} h &= 1.50\ut{m}\\ \Delta x &= 1.52\ut{m}\\ \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ (a) $t=?$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ -1.5 &= (0)t+\frac{1}{2}(-g)t^2\\ 1.5 &= \frac{1}{2}gt^2\\ \end{aligned}$$ $$\begin{aligned} t&=\sqrt{\frac{3}{g}}\\ &\approx 0.553095709524\ut{sec}\\ &\approx 0.553\ut{sec}\\ \end{aligned}$$ (b) $v_0=?$ $$\b..

$$\begin{cases} \vec v_0 &= 6.75\i\ut{m/s}\\ \Delta \vec r &= -5.00\j\ut{cm}\\ \vec a &= -g\j\\ g &\approx 9.80665\ut{m/s^2}\\ \end{cases}$$ $$ \Delta x =? $$ $$\begin{aligned} \Delta y &= v_{y0}t+\frac{1}{2}a_yt^2,\\ -5.00\times10^{-2} &= 0\cdot t+\frac{1}{2}(-g)t^2\\ 5.00\times10^{-2} &= \frac{1}{2}gt^2\\ t&= \frac{1}{\sqrt{10g}} \end{aligned}$$ $$\begin{aligned} \Delta x &= v_x t = v_0 t\\ &=..

$$\begin{cases} A_y&=30\ut{m}\\ \vec v_A&=3.0\i\ut{m/s}\\ \vec v_{B0}&=0\\ \abs{\vec a_{B}}&=0.40\ut{m/s^2}\\ \end{cases} $$ $$ \begin{aligned} \vec r_A &=\Delta \vec r_A + \vec r_{A0}\\ &=\int \vec v_A\dd t+\vec r_{A0}\\ &=\int 3\i\dd t+30\j\ut{m}\\ &=3t\i+30j\ut{m}\\ \end{aligned} $$ $$ \vec a_B = \frac{2}{5}\sin\theta\i+\frac{2}{5}\cos\theta\j\ut{m/s^2}$$ $$ \begin{aligned} \vec v_B&=\vec v_{..

$$\begin{cases} \vec a&=3t\i+4t\j\ut{m/s^2}\\ \vec r_0&=20.0\i+40.0\j\ut{m}\\ \vec v_0&=5.00\i+2.00\j\ut{m/s}\\ \end{cases} $$ $$ \begin{aligned} \vec v&=\Delta \vec v+\vec v_0\\ &=\int_0^t \vec a\dd t+\vec v_0\\ &=\int_0^t 3t\i+4t\j\dd t+\vec v_0\\ &=\(\frac{3}{2}t^2+5\)\i+\(2 t^2+2\)\j\\ \end{aligned} $$ $$ \begin{aligned} \vec r&=\Delta \vec r+\vec r_0\\ &=\int_0^t \vec v\dd t+\vec r_0\\ &=\i..

$$\begin{cases} \vec a&=5.00\i+7.00\j\ut{m/s^2}\\ \vec v_0&=4.00\i\ut{m/s}\\ \end{cases} $$ $$t_{\Delta x=10}=?$$ $$ \begin{aligned} \Delta r_x &= v_{x0}t+\frac{1}{2}a_xt^2\\ 10 &= 4t+\frac{1}{2}\cdot5t^2\\ t_{\Delta x=10}&=\frac{2}{5} \left(\sqrt{29}-2\right) \end{aligned} $$ $$v_{\Delta x=10}=?$$ $$ \begin{aligned} \vec v&=\vec v_0 + \vec a t,\\ \vec v_{\Delta x=10}&=\vec v_0 + \vec a t_{\Delt..

$$\begin{cases} \vec a&=6.0\i-3.0\j\ut{m/s^2}\\ \vec v_0&=12.0\i+18.0\j\ut{m/s}\\ \end{cases} $$ $$ \begin{aligned} \vec v&=\vec v_0+\vec a t\\ &=12.0\i+18.0\j+(6.0\i-3.0\j)t\ut{m/s}\\ &=(12.0+6.0t)\i+(18.0-3.0t)\j\ut{m/s}\\ \end{aligned} $$ $$v_y=18.0-3.0t=0$$ $$t=6\ut{s}$$ $$ \begin{aligned} \vec v_6&=(12.0+6.0\cdot6)\i+(18.0-3.0\cdot6)\j\ut{m/s}\\ &=48\i\ut{m/s} \end{aligned} $$